Calculus: Early Transcendentals, Chapter 7, 7.2, Section 7.2, Problem 32

inttan^2(x)sec(x)dx
use the identity:tan^2(x)=sec^2(x)-1
inttan^2(x)sec(x)dx=int(sec^2(x)-1)sec(x)dx
=int(sec^3(x)-sec(x))dx
Now apply the Integral Reduction:intsec^n(x)dx=(sec^(n-1)(x)sin(x))/(n-1)+(n-2)/(n-1)intsec^(n-2)(x)dx
intsec^3(x)dx=(sec^2(x)sin(x))/2+1/2intsec(x)dx
Use the common integral:intsec(x)dx=ln(tan(x)+sec(x))
:.inttan^2(x)sec(x)dx=(sec^2(x)sin(x))/2+1/2intsec(x)dx-intsec(x)dx
=(sec^2(x)sin(x))/2-1/2intsec(x)dx
=(sec^2(x)sin(x))/2-1/2ln(tan(x)+sec(x))
add a constant C to the solution,
=(sec^2(x)sin(x))/2-1/2ln(tan(x)+sec(x))+C

What is the dramatic irony in A Modest Proposal?

Jonathan Swift's "A Modest Proposal" is filled to the brim with verbal irony, not dramatic irony. Verbal irony is when you say the opposite of what you really mean, and Swift uses it to point out that the English should treat the Irish better.
For example, he uses verbal irony to argue that the fact that so many poor Irish people are starving and sick is a good thing because, as they succumb to famine and illness, the problem will essentially take care of itself:

Some persons of a desponding spirit are in great concern about that vast number of poor people, who are aged, diseased, or maimed, and I have been desired to employ my thoughts what course may be taken to ease the nation of so grievous an encumbrance. But I am not in the least pain upon that matter, because it is very well known that they are every day dying and rotting by cold and famine, and filth and vermin, as fast as can be reasonably expected.

In other words, once the impoverished Irish all die off, there won't be an Irish problem anymore. It's an idea that's ridiculous and cruel, and that's exactly the point. Swift's use of verbal irony shines a harsh light on the injustices and injuries inflicted upon the Irish by the English and makes the case that conditions need to change.

Let's first define irony and see if there is dramatic irony in this particular writing. 
Irony is what is known as a "figure of speech," which means that words are said, but you cannot take their meaning at face value. This means also that the intended meaning of the word is not the same as its actual meaning; rather, it potentially means the opposite.
Irony occurs in everyday life. In any given situation, irony occurs when the result is completely different from what people thought it was going to be.
In literature, we have a few types of irony:
Verbal is the type of irony explained previously, where words mean something totally different than what their original meaning entails.
If this is the type of irony you are looking for, then Jonathan Swift is your answer. "A Modest Proposal" is neither modest nor should it exist as a proposal. At the same time, it is not intended to be one; it is a macabre, long satire written by Swift in a way that we can equate with the likes of Jon Stewart, Stephen Colbert ,and all the other sarcastic comedians who say things when they really mean the opposite. In fact, the entire piece is ironic in nature.

I have been assured by a very knowing American of my acquaintance in London, that a young healthy child well nursed, is, at a year old, a most delicious nourishing and wholesome food, whether stewed, roasted, baked, or boiled; and I make no doubt that it will equally serve in a fricasie, or a ragoust.

Imagine if he were serious about this!
Situational irony is what we also described previously, where something happens that nobody expected to happen because they thought that the exact opposite would result. For example, suppose that a villain is plotting the end of a superhero, only to have the entire plan fall upon him, making him his own victim. This is irony in a situation. 
Now, let's return to your question on dramatic irony. In dramatic irony, something will happen to a character that you, as the audience, are aware of, but the character is not. Think about a play where you already know that the ending will be tragic, but the characters are oblivious to it. 
Like the title says, "A Modest Proposal" is an essay that supposedly attempts to provide a solution to the "Irish problem" and the issues of poverty taking place at the time. It is a satirical speech, which does not include a plot, nor characters. For this reason, there is no dramatic irony in this work, and there could not be unless Swift had told us a tale of someone to which something happens that everyone else expected, except that very person. This being said, the type of irony in "A Modest Proposal" is mainly verbal, and not dramatic. 

What is Dexter's motivation for being a caddy? How does this make Dexter different from some of the other caddies?

One of Dexter’s motivations for caddying, beyond the pursuit pocket money, is related to his desire to achieve success greater than that of most people in his Minnesota town. His feelings about his station in life can be seen in Fitzgerald’s use of imagery early in the story, when Dexter is detailing his feelings during the cold months:

The country gave him a feeling of profound melancholy—it offended him that the links should lie in enforced fallowness, haunted by ragged sparrows for the long season. It was dreary, too, that on the tees where the gay colors fluttered in summer there were now only the desolate sand-boxes knee-deep in crusted ice.

In contrast, he viewed Sherry Island, where he caddied, as a place where dreams came true. In the fall, when the beautiful colors of summer had faded, he would play out summer victories in his imagination:

He became a golf champion and defeated Mr. T. A. Hedrick in a marvellous match played a hundred times over the fairways of his imagination, a match each detail of which he changed about untiringly—sometimes he won with almost laughable ease, sometimes he came up magnificently from behind. Again, stepping from a Pierce-Arrow automobile, like Mr. Mortimer Jones, he strolled frigidly into the lounge of the Sherry Island Golf Club—or perhaps, surrounded by an admiring crowd, he gave an exhibition of fancy diving from the spring-board of the club raft.

Dexter‘s ambitions play a central role in Winter Dreams, and caddying serves as a launching pad for the rest of his life.

Dexter in F. Scott Fitzgerald's "Winter Dreams" "caddied only for pocket money" (Fitzgerald, 1). Dexter does not need to caddy, because his father "owned the second best grocery-store in Black Bear" (Fitzgerald, 1). However, he is the best caddy at the club, and the money is good. He is often requested by some of the better golfers at the club, and "the thirty dollars a month he earned through the summer were not to be made elsewhere around the lake" (Fitzgerald, 2). Dexter does not really need the money, though, and so he decides to quit one morning right in the middle of his shift.
For the other caddies, however, this is not just a summer job or a hobby but money that they desperately need. The opening of the text explains that "some of the caddies were poor as sin and lived in oneroom houses with a neurasthenic cow in the front yard" (Fitzgerald, 1).
https://public.wsu.edu/~campbelld/engl494/winterdreams.pdf

How does the street between the sniper and his target function as a symbol in the short story, "The Sniper?"

On a street in downtown Dublin during the Irish Civil War a Republican sniper is posted on a rooftop in Liam O'Flaherty's short story "The Sniper." Opposite him on the other side of the street is a Free State sniper. The street which separates them is a symbol of the division between the Irish who wanted complete freedom from the British, Republicans, and those that were willing to accept being part of the British Commonwealth, Free Staters. More than that it is symbolic of the disagreement which brewed between people who had once been allied. After all, the Free Staters were once part of the Irish Republican Army and the division in the army often involved a clash of those from the same family.
It is noteworthy that the enemy armored car stops on "the opposite side of the street" from the Republican sniper. The lines between the two foes is symbolically drawn, and when an old woman appears to tell the armored car commander the position of the Republican, both her and the commander are killed by the sniper. Ultimately the sniper kills his opponent on the opposite rooftop. For a brief time he is overcome by regret but soon pulls himself together and decides to cross the street, at great peril, to identify his victim. The crossing of the street is an acknowledgement that these two men were, in reality, brothers, and that the street (or war) should have never divided them.

When does Miss Strangeworth stop calling Mr. Lewis "Tommy"?

Miss Strangeworth is very old-fashioned and particular about how people should address one another. She sees herself as the keeper of the flame concerning social etiquette in the town, a living connection to an idealized past, in which people were much more formally polite. That's why she stops calling Mr. Lewis by his Christian name. In Miss Strangeworth's prim and proper world, one simply doesn't address adults outside of one's family with such a degree of familiarity.
What we see here is evidence of Miss Strangeworth's double standards when it comes to social etiquette. Though outwardly the epitome of old-fashioned good manners, she's actually a mean, nasty old woman sending vicious poison-pen letters to anyone in the town she doesn't like. There are clearly two Miss Strangeworths at work here, and her insistence on calling Tommy Mr. Lewis highlights the stark contrast between the two—between the respectable face she presents to the world and her much darker interior self.

In "The Possibility of Evil," Miss Strangeworth stopped using Mr Lewis's name, "Tommy," on the day that he left high school and started working in the grocery. Likewise, it was also at this time that Mr Lewis stopped calling Miss Strangeworth by her first name, "Addie."
Evidently, for Miss Strangeworth, Tommy's move from high school to the workplace symbolised the end of their childhood friendship. In her mind, Mr Lewis was now a respectable member of her town and should be addressed accordingly.
Moreover, in referring to the fact that Mr Lewis is in the grocery while Miss Strangeworth is "living alone" suggests that a romantic connection had once occurred and that Mr Lewis's move to the grocery brought it to an end. By calling him "Mr Lewis," Miss Strangeworth, therefore, reinforces the end of his connection and the beginning of a more formal and business-like relationship.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 60

The given sequence is:
-1, 8 , 23, 44, 71, 104
To determine if it is a linear sequence, take the difference between consecutive terms.
-1, 8 , 23, 44, 71, 104
vvv vvv vvv vvv vvv
9 1521 27 33
Notice that the result are not the same. So the sequence is not linear.
Then, take the second difference of the consecutive terms to determine if it is quadratic.
9, 15, 21, 27, 33
vvv vvv vvv vvv
6 6 6 6
Since the second difference of the consecutive terms are the same, the sequence is quadratic.
To determine the model of the quadratic expression apply the formula:
T_n = an^2 + bn + c
where Tn is the nth term of the sequence.
To solve for the values of a, b and c, consider the first few three terms of the sequence.
Plug-in T1=-1 and n=1.
-1=a(1)^2+b(1)+c
-1=a+b+c (Let this be EQ1.)
Also, plug-in T2=8 and n=2.
8=a(2)^2 + b(2) + c
8=4a+2b+c (Let this be EQ2.)
And, plug-in T3=23 and n=3.
23=a(3)^2+b(3)+c
23=9a+3b+c (Let this be EQ3.)
Then, apply elimination method of system of equations. Let's eliminate variable c.
To eliminate c, subtract EQ2 from EQ1.
EQ1: -1=a+b+c
EQ2: -(8=4a+2b+c)
-----------------
-9 = -3a -b
And simplify the resulting equation.
-9=-3a-b
9=3a+b (Let this be EQ4.)
Eliminate c again. So subtract EQ3 from EQ1.
EQ1: -1=a+b+c
EQ2: -(23=9a+3b+c)
-----------------
-24=-8a-2b
And, simplify the resulting equation.
-24=-8a-2b
12=4a+b (Let this be EQ5.)
Then, eliminate another variable. Let it be c.
To eliminate c, subtract EQ4 from EQ5.
EQ5: 12=4a+b
EQ4: -(9=3a+b)
--------------
3=a
Now that the value of a is known, plug-in it to either EQ4 or EQ5. Let's use EQ4.
9=3a+b
9=3(3)+b
0=b
Then, plug-in the value of a and b to either EQ1, EQ2 or EQ3. Let's use EQ1.
-1=a+b+c
-1=3+0+c
-4=c
Now that values of a, b and c, plug-in them to the formula of nth term of quadratic expression.
T_n=an^2+bn+c
T_n=3n^2+(0)n+(-4)
T_n=3n^2-4
Therefore, the given -1, 8 , 23, 44, 71, 104 is a quadratic sequence. The model for its nth term is T_n=3n^2-4 .

In Rossetti's "Song," how does mourning over death increase misery?

In "Song," Rossetti believes death to be a liberating experience.  Mourning over it is not necessary because it would increase misery.
As the poem's speaker, Rossetti is quite open that when she does die, the "dearest" left behind should "sing no sad songs" over her passing.  She gives instruction to "plant... no roses at my head."  Rossetti feels that there is an inevitability to death.  Mourning over it is not necessary: "Haply I may remember, / And haply may forget."  Death is a natural condition of being in the world.  At the same time, Rossetti sees death as a freeing experience.  When she writes that she will no longer "feel the rain" or hear the nightingale / Sing on, as if in pain," it is an indication that death will free her from the pain and hurt that is a part of the living world.  Rossetti would argue that to mourn over it causes unnecessary pain when it should be seen as something liberating.  
In the concluding line to another one of Rossetti's poems, "Remember," she writes that we should not "remember and be sad."  "Song" conveys a similar attitude towards mourning.  For Rossetti, mourning brings extended and inappropriate sadness to an experience that transcends attachment.  

How does Salinger use clothing and physical appearance to develop Robert Ackley?

We never learn what Ackley wears, but we do learn about his physical appearance. He is tall and round-shouldered with pimples and mossy teeth. He cuts his nails in Holden's room, and Holden has to keep telling him not to get the nail clippings on the floor. Holden thinks of him as "peculiar."
Ackley's appearance reflects his awkwardness and his lack of social skills. He doesn't seem to be able to see himself as others see him. For example, he doesn't seem to realize he might get along better with people if he brushed his teeth. He also doesn't seem to realize that Holden doesn't want to talk to him when he barges into his room, even though Holden doesn't look up from his book and later puts his hunting cap over his eyes. Even when Ackley is "nosy," as Holden puts it, he lacks sensitivity in how to approach other people.
Ackley, a slob, resents Stradlater, who is able to present himself well even though Holden characterizes him as a "secret slob." Ackley seems to wish he could act like Stradlater while insisting he hates him.
Holden feels sorry for Ackley and recognizes that they are both outsiders, so he invites him to the movies. At the end of the novel, he remembers Ackley and says he misses him sometimes.

Robert Ackley, Holden Caulfield's next-door neighbor in his boarding school dorm, is described as having terrible hygiene. He is described as having terrible acne and foul teeth/breath. In one scene, he goes so far as to clip his toenails all over Holden's floor. Salinger uses Ackley's gross, unhygienic appearance and behavior, and Holden's disgust at these things, to comedic effect. That Ackley is so unappealing also serves to explain why Holden doesn't like him, doesn't want to be around him, and gets so annoyed when he comes into his room (often unannounced and uninvited).
Ackley is described as pompous and acts as though he believes himself to be better than Holden. This attitude does not match up to Ackley's physical appearance and lack of self-care. He acts high and mighty, but it's doubtful when he last took a shower.

What is happening to the value of the U.S. dollar these days?

It's possible to answer this question in any number of ways. There are many influences that affect the value of currency in international markets; and the dollar, being the standard and most widely-used and traded currency around the world, is affected by activity in other currencies.
For example, the recent BREXIT decision in the UK has affected world currency values, as this decision on the part of Great Britain to leave the European Union means there will be changes in their banking system. The value of the pound against the dollar experienced dramatic change when the results of this vote were announced a few weeks ago, and it is believed that as the process of leaving the European Union continues, the value of the pound will continue to be unstable.  Because London is a major banking and commerce capital of the world, it is a hub for world markets and the US-based markets respond accordingly to developments in the UK.
The dollar is currently fairly strong, possibly because the recent jobs report was fairly positive. The state of jobs and new construction are factors that afec the value of the dollar, as well as world events linked to terrorism. The reason terrorism affects world markets is that states of emergency affect world travel and tourism, which then impacts commerce directly.
The decision of the Federal Reserve to raise or lower interest rates is also a factor that affects the value of the dollar. The Fed has declined to raise interest rates for a number of years but financial forecasters are generally in agreement that interest rates will be going up fairly soon.
 
https://www.forexcrunch.com/category/forex-weekly-outlook/us-dollar-forecast/

In "Thank You, M'am," where do you see a turning point for Roger in terms of his character?

There are two turning points for Roger's character in "Thank You, M'am." The first is where Roger chooses to stay with Mrs. Jones and wash his face as told to do: "Roger looked at the door—looked at the woman—looked at the door—and went to the sink." The second turning point provides the resolution of the story where, when Mrs. Jones and he are both overcome with emotion, he can manage only to say "Thank you" as she ushers him out onto her "barren stoop" and the street.

"Good-night! Behave yourself, boy!" she said, looking out into the street.
The boy wanted to say something else other than "Thank you, m’am" to Mrs. Luella Bates Washington Jones, but he couldn’t do so as he turned at the barren stoop and looked back at the large woman in the door.

At the first turning point for Roger's character, Roger rejects running out the open door and instead chooses trusting Mrs. Jones and accepting her offer to share her meal with him. He turns from petty theft and fear and toward Mrs. Jones's compassion and care. It's as though he is thinking—or feeling—that he wishes he were her son and that she would teach him "right from wrong" and that she would make sure he had a clean face and meals to eat.


He looked as if he were fourteen or fifteen, frail and willow-wild, in tennis shoes and blue jeans.
 
The woman said, "You ought to be my son. I would teach you right from wrong. Least I can do right now is to wash your face. Are you hungry?"

At the second turning point for Roger's character—following their supper during which Mrs. Jones tells him about her job in the late-night "hotel beauty-shop" and during which she says, "Eat some more, son"—Roger comes to understand the meaning of Mrs. Jones's remark that he could have asked her for those "blue suede shoes" instead of snatching her "pocketbook." Puzzled at first ("M'am?"), he comes to learn about understanding, generosity, and compassion when she gives from the little she has. Because Mrs. Jones hands him ten dollars for "some blue suede shoes," he wants to say something heartfelt and grateful, but all he can manage is a quiet "Thank you." He turns from feeling alone and turns to feeling like part of a shared life.

"Now, here, take this ten dollars and buy yourself some blue suede shoes. And next time, do not make the mistake of latching onto my pocketbook nor nobody else’s—"

What role does religion play throughout the novel? What effect does it have on the lives and feelings of the characters?

To be honest, religion plays a fairly minor role in terms of affecting characters throughout the story. Very little narrative time is spent on church topics, attending worship, explaining differences between religions, or depicting specific bible references. That isn't to say that religion doesn't have an impact on the narrative plot. Holling Hoodhood is part of a Presbyterian family; however, everybody else in his school is either Catholic or Jewish. On Wednesday afternoons, the Catholic students go to Catechism and the Jewish students go to their religious studies course. This leaves Holling at school alone. The school's solution is to put him in Mrs. Baker's classroom. She is essentially a babysitter, and she and Holling both don't like the arrangement. She makes him do boring manual labor tasks like clean erasers. Eventually, Mrs. Baker begins teaching Holling Shakespeare during the Wednesday afternoons, and the relationship grows into a very deep and powerful relationship. Religion mainly served as a way to get Holling and Mrs. Baker in a classroom together in order to propel the character development forward.

College Algebra, Chapter 2, 2.1, Section 2.1, Problem 56

If point $M$ is the midpoint of the segment $AB$. Show that $M$ is equidistant from the vertices of triangle $ABC$




If $M$ is the midpoint of segment $AB$, then its coordinates is $\displaystyle \left( \frac{a}{2}, \frac{b}{2} \right)$
Thus, by using distance formula,

$
\begin{equation}
\begin{aligned}
d_{MA} &= \sqrt{\left( a- \frac{a}{2} \right)^2 + \left( 0 - \frac{b}{2} \right)^2 }\\
\\
d_{MA} &= \sqrt{\left( \frac{a}{2} \right)^2 + \left( - \frac{b}{2} \right)^2 }\\
\\
d_{MA} &= \sqrt{\frac{a^2}{4} + \frac{b^2}{4} }\\
\\
d_{MA} &= \frac{\sqrt{a^2 + b^2}}{2} \text{ units}
\end{aligned}
\end{equation}
$


Similarly,

$
\begin{equation}
\begin{aligned}
d_{MB} &= \sqrt{\left( 0- \frac{a}{2} \right)^2 + \left( b - \frac{b}{2} \right)^2 }\\
\\
&= \sqrt{\left( -\frac{a}{2} \right)^2 + \left( \frac{b}{2} \right)^2 }\\
\\
&= \sqrt{\frac{a^2}{4} + \frac{b^2}{4} }\\
\\
&= \frac{\sqrt{a^2 + b^2}}{2} \text{ units}
\end{aligned}
\end{equation}
$


And,

$
\begin{equation}
\begin{aligned}
d_{MC} &= \sqrt{\left( 0- \frac{a}{2} \right)^2 + \left( b - \frac{b}{2} \right)^2 }\\
\\
d_{MC} &= \sqrt{\left( -\frac{a}{2} \right)^2 + \left( - \frac{b}{2} \right)^2 }\\
\\
d_{MC} &= \sqrt{\frac{a^2}{4} + \frac{b^2}{4} }\\
\\
d_{MC} &= \frac{\sqrt{a^2 + b^2}}{2} \text{ units}
\end{aligned}
\end{equation}
$


It shows that $M$ is equidistant from the vertices of triangle $ABC$.

sum_(n=1)^oo 1/(nsqrt(n^2+1)) Use the Limit Comparison Test to determine the convergence or divergence of the series.

Recall Limit Comparison Test considers two positive series a_ngt=0 and b_ngt 0 for all n such that the limit from the ratio of two series as:
lim_(n-gtoo)a_n/b_n=c
 where c is positive and  finite ( 0ltcltoo) .
When we satisfy the condition for the limit value,  the two series will have the same properties. Both will either converge or diverges. We may also consider the conditions:
 If  we have  lim_(n-gtoo)a_n/b_n=0 , we follow: sum b_n converges then sum a_n converges.
 If  we have lim_(n-gtoo)a_n/b_n=oo , we follow: sum b_n diverges then sum a_n diverges.
 For the given series sum_ (n=1)^oo 1/(nsqrt(n^2+1)) , we may let a_n= 1/(nsqrt(n^2+1)).
Rationalize the denominator:
1/(nsqrt(n^2+1)) *sqrt(n^2+1)/sqrt(n^2+1) =sqrt(n^2+1)/(n(n^2+1)
Note: sqrt(n^2+1)*sqrt(n^2+1) = (sqrt(n^2+1))^2 = n^2+1 .
Ignoring the constants, we get:
sqrt(n^2+1)/(n(n^2+1)) ~~sqrt(n^2)/(n(n^2)) or 1/n^2
Note: sqrt(n^2) =n . We may cancel it out to simplify.
This gives us a hint that we may apply comparison between the two series: a_n= 1/(nsqrt(n^2+1)) and  b_n = 1/n^2 .
 The limit of the ratio of the two series will be:
lim_(n-gtoo) [1/(nsqrt(n^2+1))]/[1/n^2] =lim_(n-gtoo) 1/(nsqrt(n^2+1))*n^2/1
                       =lim_(n-gtoo) n^2/(nsqrt(n^2+1))
                        =lim_(n-gtoo) n/sqrt(n^2+1)
Apply algebraic techniques to evaluate the limit. We divide by n with the highest exponent which is n  or n^1 . Note: n is the same as sqrt(n^2)  .
lim_(n-gtoo) n/(sqrt(n^2+1)) =lim_(n-gtoo) (n/n)/(sqrt(n^2+1)/sqrt(n^2))
                      =lim_(n-gtoo) 1/sqrt(1+1/n^2)
                      =1/sqrt(1+1/oo)
                      = 1/sqrt(1+0)
                      = 1 /sqrt(1)
                      = 1/1
                      =1
 The limit value c=1 satisfies  0ltclt oo .   
 Apply the p-series test: sum_(n=1)^oo 1/n^p is convergent if  pgt1 and divergent if plt=1 .
The sum_(n=1)^oo 1/n^2  has p =2 which satisfy pgt1 since 2gt1 . Then, the series sum_(n=1)^oo 1/n^2  is convergent.
Conclusion based from limit comparison test:
With the series sum_(n=1)^oo 1/n^2  convergent, it follows the series sum_ (n=1)^oo 1/(nsqrt(n^2+1)) is also convergent.

How did World War I become a "total war"?

The American-English Dictionary defines total war as "war that is unrestricted in terms of the weapons used, the territory or combatants involved, or the objectives pursued, especially one in which the laws of war are disregarded." By that definition, World War I was certainly a prime example of total war. For this was a war the likes of which had never been seen before, involving the governments, economies, and civilian populations of the respective combatants to an unprecedented extent.
Previously, wars had tended to be relatively small affairs with limited aims, fought purely between the relevant combatants' armies. In World War I, however, that changed completely. War was no longer just a matter for soldiers, but for civilians as well. Now whole nations became involved in the military struggle. Every single aspect of national life was geared towards winning the war.
In Britain, for example, the government became involved in the running of the economy to a hitherto unimaginable extent. The government set production targets for armaments and munitions, nationalized factories, and allocated manpower and resources.
In Germany, meanwhile, the conscription of labor became a major part of the war effort. Under the so-called Auxiliary Service Law of 1916, the German government was given sweeping powers to employ and relocate any number of adult male citizens to satisfy the growing demands of a wartime economy operating at near full capacity.
Total war overturned many of the old social and political certainties, not just in relation to the role of the state in economic management. In Britain, somewhere between 700,000 and 1 million women were employed in munitions factories, manufacturing much-needed weapons for the British armed forces. Previously, such work was regarded as unsuitable for women and was the sole preserve of men. But with men desperately needed at the front, the Ministry of Munitions drafted women workers to help fill the gap created by mass conscription.
During the War, Britain, Germany, and a number of other countries witnessed a vast expansion of the state's police power. The exigencies of war-time permitted governments to arrogate to themselves a vast panoply of new powers, from the censorship of newspapers to the imprisonment of civilians without trial. Governments also greatly expanded surveillance and counter-subversion networks, designed to root out those considered a clear and present danger to national security. The systematic curtailment of civil liberties during wartime became a widespread feature among European democracies and, also, the United States. The demands of total war could be used as a pretext for governments to suppress radical political groups and movements, who would normally be protected by the rule of law.

Evidence that Anne Frank doesn’t like her mom.

It is fair to say that the relationship between Anne and her mother is not particularly close. Anne's diary is full of examples of conflict between them. It is not simply that they get on each other's nerves in such a tense, claustrophobic environment, Anne also does not really have any respect for her mother:

I need my mother to set a good example and be a person I can respect, but in most matters she's an example of what not to do.

Part of the problem is that Anne is very much her father's little girl, and she wants to feel the same kind of loving warmth from Edith that she receives from Otto. Yet, Anne sees her mother as cold and unapproachable. There is clearly a clash of personalities here. Anne is vivacious and full of fun, whereas Edith takes life more seriously. However, this is not surprising when one considers the fraught situation in which the Franks find themselves.
Edith never comes across as a bad person; she just has a completely different personality from her daughter. One gets the impression that Anne and Edith could well have worked out their differences had they been given the proper time and space.

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 44

At what rate is the distance between the tips of the hands changing at one'o clock
Given that the hour hand of a watch is 4mm long and the minute hand is 8mm long. Determine how fast is the distance between the tips of the hand changing at an one o' clock?

For our strategy, we will use the law of cosines to relate the length of the sides and the distance between the tips of the hands. Also, both of the hands are moving at constant rates so the angle between them is also changing at a constant rate.

Law of cosines: $a^2 = b^2 + c^@ - 2(b)(c) \cos \theta \qquad \Longleftarrow \text{ Equation 1}$

$
\begin{equation}
\begin{aligned}
\text{we let } a & \text{ be the distance between the tips of the hands}\\
b & \text{ be the length of the hour hand}\\
c & \text{ be the length of the minute hand}\\
\theta & \text{ be the angle between the hands}
\end{aligned}
\end{equation}
$


At one o' clock, the angle between the hands is $30^\circ$, $\displaystyle \frac{360}{12} = 30^\circ$


$
\begin{equation}
\begin{aligned}
a^2 &= 4^2 + 8^2 - 2(4)(8) \cos (30)\\
a &= 4.9573 \text{ mm} && \text{, the distance between the tips precisely at one o' clock}
\end{aligned}
\end{equation}
$


Notice that in Equation 1, the only variables that change are $a$ and $\theta$,
Now we differentiate Equation 1 with respect to time...
$\displaystyle 2a \frac{da}{dt} = -2 bc(-\sin \theta) \frac{d \theta}{dt}$


Solving for $\displaystyle \frac{da}{dt}$
$\displaystyle \frac{da}{dt} = \frac{bc \sin \theta}{a} \left( \frac{d \theta}{dt} \right) \qquad \Longleftarrow \text{ Equation 2}$

To solve for $\displaystyle \frac{d \theta}{dt}$, now the angle is changing with respect to time, note that the hour hand makes one revolution every hour in the clockwise direction. Hence, the hour hand angle has a rate of change of $2 \pi$ radians every 12 hours and is equal to $\displaystyle \frac{2\pi}{12} = \frac{\pi}{6} \text{rph}$ (radians per hour). Also, the minute hand has an angle that changes by $2 \pi$ radians every hour and is equal to $2 \pi$ rph. Thus, the relative velocity of the two hands is then $\displaystyle \frac{\pi}{6} - 2 \pi = \frac{-11\pi}{6} \text{rph}$ the value is negative because it is always the hour hand that takes the lead from the minute hand.
So $\displaystyle \frac{d \theta}{dt} = \frac{-11 \pi}{6}$, using this to solve for the rate of change of the distance between the tips of the hands in Equation 2.

$
\begin{equation}
\begin{aligned}
\frac{da}{dt} &= \frac{bc \sin \theta}{a} \left( \frac{d\theta}{dt} \right)\quad ; \theta = 30^\circ\\
\\
\frac{da}{dt} &= \frac{4(8) \sin (30)}{4.9573} \left( \frac{-11 \pi}{6} \right)
\end{aligned}
\end{equation}
$


$\boxed{\displaystyle \frac{da}{dt} = -18.59 \frac{\text{mm}}{h}}$

Who is the most ancient inhabitant of the village and what does he affirm?

The answer to this question can be found near the story's conclusion. The "ancient" village person that this question is asking about is Peter Vanderdonk.

Peter was the most ancient inhabitant of the village, and well versed in all the wonderful events and traditions of the neighborhood.

Peter's role in the story is small, but it is important. Rip has just come back from his extended sleep; however, nobody believes his story. They think it is the ramblings and fantasy of an old man. Peter is a wise and respected ancestor of an important historian in the town, and Peter says that it is a fact that the Kaatskill mountains had always been haunted by strange beings. Hendrick Hudson and his crew are such beings, and even Peter's own father claimed to have seen them playing nine-pins. With Peter's testimony of support for Rip's story, Rip is now believed. He lives out the rest of his days doing what he always did best—telling kids stories.

The oldest inhabitant of the village in "Rip Van Winkle" is Peter Vanderdonk. When Rip returns to the village after twenty years and says he has been asleep all that time, many don't believe his story of stumbling on ancient Dutch people and being enchanted. Many also don't believe he is Rip, even though an old woman recognizes him.
Peter, however, has more authority than the old woman, because his father was a historian who wrote an early account of the area and because he himself is "well versed" in the traditions and history of the region. Peter both affirms that Rip is who he says he is and that it is well-known that the mountains have long been haunted. Peter says that his own father saw people in old Dutch clothes playing nine-pins in the mountains, just as Rip says.
With this matter settled, the villagers turn back to the more important issue of the election.

How does cruelty play an important role in the destruction of love and in the novel as a whole?

Cruelty runs through the novel. The cruelties Heathcliff suffers as a child and adolescent harden him. He is adopted, favored by his stepfather, and then, after the stepfather dies, he is abused and degraded by his stepbrother. He and his stepsister Catherine develop a strong bond and love each other, but Catherine treats him cruelly when she marries the wealthy Edgar Linton rather than him. Heathcliff also suffers when Catherine dies.
Because of how he has suffered at the hands of the Earnshaws and Lintons, Heathcliff wants revenge on the two families. Therefore, he treats Isabella Linton, the woman he marries, with sadistic cruelty, wanting her to hate him. He also mistreats Cathy, Catherine and Edgar's daughter, after he and Isabella manipulate her into marrying their son.
Bronte shows how abused children become abusive adults.

What are the qualities of "Second Anne" that are revealed to us? How is she different from "Ordinary Anne"?

"Second Anne" is the sensitive, reflective part of Anne's character. Anne calls it her "better," "purer," "deeper," and "finer" side. This part of Anne makes her grieve over the pain of people she loves, such as her late grandmother, who died of a terminal illness, and an old friend who is in a concentration camp (Wednesday, 29 December 1943, and Saturday, 27 November 1943). The "deeper Anne" recognizes all the misery and cruelty in her world but still believes "that people are truly good at heart" and hopes to realize her ideals someday (Saturday, 15 July 1944).
Like "Second Anne," "Ordinary Anne" sees plenty of "joy in life" (Tuesday, 1 August 1944). But Anne feels that her surface side is "what a romantic film is to a profound thinker." "Ordinary Anne" spends her time joking, flirting, and entertaining; "Second Anne" thinks and writes seriously and quietly. While "Ordinary Anne" is always chattering, "Second Anne" has never spoken up in front of other people.
Anne concludes that much of her conflict with her fellow hiders results from her showing them her sassy, boisterous side rather than her kind, quiet one. But she doesn't show her inner nature to others, because she is afraid they would laugh at it. And, while the superficial Anne is used to mockery, the true Anne would be deeply wounded by ridicule.
To examine Anne's comparison of her two selves, reread her last diary entry (Tuesday, 1 August 1944).

How did the visit to Baltimore change Helen's life in a great way?

As Helen grew from toddlerhood to school age, she became increasingly frustrated at her inability to communicate her thoughts to other people. This led to frequent tantrums and meltdowns, so much so that her parents became concerned and took her to see an eye specialist in Baltimore named Dr. Chisholm in the hopes he could help her regain some eyesight. He could not, but referred the family to Alexander Graham Bell. Helen remembered visiting Bell in Washington and playing with his watch. She recalled his kindness.
Bell, in turn, referred the family to the Perkins Institute in Boston, where they were able to hire Miss Sullivan as a teacher for Helen. Helen describes Miss Sullivan's arrival in her memoir as a life-changing miracle, because, through Miss Sullivan, she learned to communicate through manual writing. Keller also maintained a long lasting friendship with Dr. Bell.

Helen's parents thought a trip to Baltimore to see a prominent oculist would be the answer to their daughter's problems. After examining Helen's eyes, Dr. Chisholm delivered disappointing news: he could not help her eyesight. He did, however, give them information that would start a chain of events. This chain of events led Mr. and Mrs. Keller to hire Miss Annie Sullivan, the woman who became Helen's teacher.
Dr. Chisholm told Mr. and Mrs. Keller that Helen "could be educated, and advised [her] father to consult Dr. Alexander Graham Bell, of Washington, who would be able to give him information about schools and teachers of deaf or blind children" (Chapter III). They visited Dr. Bell, and he referred them to Mr. Anagnos of the Perkins Institution. This was a school for the blind located in Boston. They wrote to Mr. Anagnos, and he found Miss Sullivan to be Helen's teacher. Miss Sullivan taught Helen how to communicate, which changed her life. She remained Helen's teacher and companion for decades.

What are the Administrative Search Exception issues relating to airline/airport security? How does the exception differ from usual requirements for probable cause? Use the internet or your library to locate additional information about Terry vs. Ohio. Do you agree with the courts’ decision that airport searches can be legally conducted under less stringent standards than ordinary probable cause? Why or why not?

We are all used to hearing about our Fourth Amendment rights as prescribed by the Constitution. The important condition in obtaining a warrant to conduct a search is “probable cause.” There has to be a compelling reason to believe that the person might possess something incriminating that a search would reveal.
But not all searches require a warrant. There are several situations in which officers can conduct a search without a warrant.
They believe a suspect is in possession of something that could harm others.
The suspect grants consent for the search.
The suspect has been arrested.
Something is in plain view.
Obviously, airport screening is a special situation. Potential terrorism endangers hundreds of lives when airliners are involved. So it is in the interest of public safety to search everybody that flies. This kind of search is called an administrative search exception. It would not be possible to obtain a warrant for everyone who flies, so everyone is searched even though there is no demonstrable probable cause. Lawsuits most often occur in this context when something illegal is found and prosecutors try to use it as evidence. Evidence gathered without probable cause can be thrown out.
I personally agree that it is appropriate to use the administrative search exception in situations like this because of the grave threat to human life. I also believe that people should be able to be prosecuted if illegal items are found, because consent to the search is implied by the fact that the suspect has entered the airport and attempted to board a plane, knowing they will be searched.
The Terry vs. Ohio decision states that officers may conduct a warrantless search if they have a reasonable belief that someone has or is about to commit a crime, or if they have a reasonable belief that the public's safety is endangered by this person. Sometimes this is referred to as "stop and frisk." For the same reason stated above concerning airport searches, I believe this ruling is appropriate. However, outside of the airport setting such a search must be well-justified by the officer.
 
https://administrativelaw.uslegal.com/administrative-agency-investigations/exceptions-to-the-warrant-requirement/

https://www.nap.edu/read/5116/chapter/9

https://www.nolo.com/legal-encyclopedia/search-seizure-faq.html

How does the novel Reservation Blues address Native American issues?

Reservation Blues by author Sherman Alexie addresses a variety of Native American issues. This imaginative story delves into life on the "rez" through the perspectives of its unique characters. Life on the reservation is blended with the Faust myth, creating a platform for Native American issues that has the benefit of realism as well as metaphor.
The Death of Dreams
One of the primary issues addressed in Reservation Blues is the death of dreams that is tragically common for occupants of the "rez." The musical group that forms on the "rez" experiences this death when they arrive in New York to find that they have been exploited by Phil Sheridan and George Wright. The two men have proven themselves to be volatile towards the Native American community and only interested in exploiting the musicians.
Stereotypes
Reservation Blues touches on many of the stereotypes that are harmful to Native Americans, including those that seem positive to outsiders. Groupies Betty and Veronica explain that they want to be part of Native American culture so they can be "wise and peaceful." This stereotype showcases the lack of understanding that outsiders have for the hardships faced by members of the "rez" as well as the discrimination they face from outside communities.
Diversity
Another major theme presented in Reservation Blues is the habit outsiders have of lumping all Native American cultures in together. The novel delves into the reality that each Native American nation has its own distinct culture, with even greater diversity between individual reservations. The characters in Reservation Blues find themselves in a world that flattens their multidimensional culture and renders it generic, ignoring both the good and bad aspects that make life on the "rez" unique, beautiful and often painful.
Poverty
Poverty is a major theme throughout Reservation Blues, even if it is often an unspoken one. The occupants of the "rez" face diminished economic opportunities because of where they grew up, and they often find the lack of expectations stifling. While there are many overtly oppressive and abusive characters, such as Wright and Sheridan, the "rez" is also forced to deal with the oppressive economic structures that prevent growth and lead to the continuation of poverty and other issues.
Genocide
While Reservation Blues has a relatively modern setting, it is clear that the Native American genocide of the past haunts the characters and continues to have a measurable impact on their lives. The fighting may have ended, but the new generation of Native Americans is left to pick up the pieces of their dreams and the diminished portion of land they have to call their own.
Throughout the novel, each of these issues is presented in a humorous, often satirical light. The humor in no way diminishes the severity of the issues but rather makes the narrative more relatable to the reader.

What characteristics of culture, race, and ethnicity may play a key role in diversity?

I'll go a little deeper into the previous educator's response. However, I must assert that there is no scientific basis for race. Scientists have found that, genetically, there is "no single absolute genetic difference" between an African and a European. The racial classification system that separates peoples of the world into three major groups, which the previous educator mentions, is based on anthropological research and pseudoscience from the eighteenth and nineteenth centuries. In other words, with the benefits of technology, we understand how phenotypical differences arise and we also know that much of the "science" on race from previous centuries was based on the biases of the researchers.
For instance, craniometry and phrenology—two pseudosciences—were developed in the nineteenth century. Both used skull measurements to determine personality and intelligence, and often researchers drew the conclusions that black people had less impressive skulls, thereby making them less intelligent and generally inferior. Such outdated and pseudoscientific views have persisted, however, in new ways. Ideas about race determining intelligence show up in Charles Murray's controversial book The Bell Curve and in some of the ideas expressed by the neuroscientist and writer Sam Harris.
Diversity is defined in different ways throughout the world. Countries such as France, South Africa, and particularly Brazil have complex racial classification systems that try to distinguish between mixed-race people and those who are more distinctly "African." However, this is not based on known ancestry, but on parentage and the physical expression of genes (i.e., lighter skin vs. darker skin).
The United States is an interesting place to understand what makes up diversity, particularly when examining its black population. As the previous educator mentions, a black person with some European ancestry is more likely to identify and be identified as "black." The historian and genealogist Henry Louis Gates Jr. has said that most African Americans belong to "the 20 percent club"—that is, most of them have twenty percent or more European ancestry due to the legacy of slavery. There are also people who look white but identify as either black or mixed-race. The "one-drop rule" from the antebellum era, which said that anyone with one black ancestor was black, inadvertently created a kind of solidarity among people with African ancestry who identify as black, even if their European ancestry is equal to or higher than their percentage of African ancestry.
That said, not all black people who live in the United States or who were born here come from ancestors who were slaves in the South. Some are the children of African immigrants; others are of West Indian derivation. These people have brought with them aspects of their own cultures (e.g., food, cultural traditions, religions) that have expanded our understanding of what it means to be black.
https://www.scientificamerican.com/article/race-is-a-social-construct-scientists-argue/?redirect=1&error=cookies_not_supported&code=a9d555af-3771-4e85-bd7d-4180ab31cede

Interesting question! The answers may be varied, depending on your own definitions of culture, race, and ethnicity. Sociology experts also hold varied positions regarding the three concepts. 
For example, some sociologists contend that race, culture, and ethnicity are interchangeable. Still others contend that race is a social construct, defined by tradition, bias, and personal conviction. Traditionally, race has been defined by a set of physical characteristics: eye color, skin color, blood types, facial features, and hair types, to name a few. To date, there is some consensus among anthropologists that the three major races in the world are the Caucasoid, the Negroid, and the Mongoloid. 
However, because of immigration and intermarriage, the concepts of race, ethnicity, and culture have become more difficult to define. For example, someone who is one-fourth Caucasian and three-fourths African American may be classified as African-American by some or mixed-race/biracial by others. Also, he may share some but not all of the characteristics that define his ethnic group. For example, he may share the same nationality, language, and traditions as the others in his group, but he may practice a different religious faith (or none at all). He may also hold markedly different political views than those in his ethnic group or cherish different ideas about gender. These cultural differences play a key role in diversity.
So, the characteristics of culture, race, and ethnicity that may play a role in diversity are variations in gender, religion, political persuasions, sexual orientations, and personal backgrounds. 
https://encyclopedia2.thefreedictionary.com/Racial+characteristics

https://ktdrr.org/ktlibrary/articles_pubs/ncddrwork/index.html

Calculus of a Single Variable, Chapter 2, 2.5, Section 2.5, Problem 48

xy-1=2x+y^2
Differentiating both sides with respect to x,
xy'+y=2+2y*y'
(x-2y)y'=2-y
y'=(2-y)/(x-2y)
Differentiating again with respect to x,
(d^2y)/dx^2=((x-2y)d/dx(2-y)-(2-y)d/dx(x-2y))/(x-2y)^2
(d^2y)/dx^2=((x-2y)(-y')-(2-y)(1-2y'))/(x-2y)^2
(d^2y)/dx^2=(-xy'+2yy'-2+4y'+y-2yy')/(x-2y)^2
(d^2y)/dx^2=((4-x)y'+y-2)/(x-2y)^2
Now plug in the value of y' in second derivative
(d^2y)/dx^2=(((4-x)(2-y))/(x-2y)+y-2)/(x-2y)^2
(d^2y)/dx^2=((4-x)(2-y)+(x-2y)(y-2))/(x-2y)^3
(d^2y)/dx^2=(8-4y-2x+xy+xy-2x-2y^2+4y)/(x-2y)^3
(d^2y)/dx^2=(8-4x+2xy-2y^2)/(x-2y)^3

What are some ways Odysseus from The Odyssey shows arrogance?

Odysseus shows considerable arrogance after making his cunning escape from Polyphemus, the Cyclops. Previously, our hero had demonstrated one of his more admirable traits in devising an ingenious plan whereby he and his remaining crew escaped the Cyclops's wrath by clinging to the bellies of his flock of sheep. Once safely aboard his ship, Odysseus lets arrogance get the better of him, and he taunts the hapless Polyphemus, revealing his true identity. There's really no need for Odysseus to rub it in, but he's so proud of himself for having put one over on the Cyclops that he just can't help himself. The consequences of Odysseus's arrogance will be dire. A furious Polyphemus prays to his father, the sea-god Poseidon, to exact terrible vengeance on Odysseus.

How did slavery support mercantilism in Great Britain?

Let's first start by defining mercantilism. In a nutshell, mercantilism depended on the belief that the amount of wealth in the world was static. This theory was developed in the early fifteenth century and was used as a point of reference by the European nations during the sixteenth through eighteenth centuries. Since the amount of wealth in the world was believed to be static, nations were working hard to collect as much of that wealth as possible.
Slavery was right at the center of mercantilism in Great Britain, as well as in other European nations. Great Britain created colonies all over the world, including in Africa and America. The main aim of these colonies was to control the available natural resources for the benefit of the British empire. Slaves were used as workers in British colonial farms where raw products such as sugar, cotton, and tea were produced. Mercantilist theorists believed that for a nation to be wealthy, it had to achieve a favorable balance of trade by importing less and exporting more. As a result, Great Britain used slaves to generate raw products in farms. These products were exported to throughout the empire, processed, and exported to other parts of the world as value-added products. This gave Great Britain an edge over its colonies, as well as other competing countries.
https://www.investopedia.com/ask/answers/041615/how-did-mercantilism-affect-colonies-great-britain.asp

Slavery was downright essential to mercantilism in eighteenth-century Great Britain. This was because mercantilism depended on the use of colonies to produce raw materials, particularly cash crops, for the mother country. These cash crops, with sugar being by far the most important, represented a major source of revenue for Great Britain. Other important cash crops included tobacco, rice, and indigo. These crops were imported by British merchants, and, theoretically at least, had to be carried on British ships. Slaves were absolutely essential to the production of these crops, which formed the foundation of the colonial British economy. Enslaved people labored on the sugar plantations of Barbados, the rice fields of Carolina, and the tobacco plantations of the Chesapeake producing the goods upon which the colonial economy depended. Even the slave trade itself was crucial to mercantilism, as the state, through the granting of monopolies, became not only the biggest consumer of cash crops and seller of manufactured goods, but the biggest supplier of labor as well. 
http://www.bbc.co.uk/history/british/empire_seapower/barbados_01.shtml

Why does Friar Laurence agree to marry Romeo and Juliet?

Friar Laurence, a peace loving man, has witnessed the conflict between the two families and the effect this conflict is having on life in Verona. As a man who seeks to do good he would have seized the opportunity to bring peace to the streets of Verona. Unfortunately he was not to know that his efforts to resolve the conflict would bring about the tragedy that was to end the lovers' lives.
As Romeo's confessor and confidant he was also aware of the pain the young man was enduring due to his unrequited love for Rosalind. Romeo, after his meeting with Juliet, presents himself as a changed man The man who locked himself in daily darkness is now filled with energy and enthusiasm for life. Marrying Juliet would guarantee that he could continue in this state. Friar Laurence cares for Romeo and in his desire to help him agrees to marrying the couple.

Audiences are told right away that a violent and long-standing feud has been going on between the Montague family and the Capulet family. This is an important piece of information regarding the Friar's decision to help Romeo and Juliet get married. In act 2, scene 3, Romeo visits the Friar and declares his love for Juliet. The Friar is rightly surprised. Romeo had just been there complaining about Rosaline and the fact that she doesn't love him back. Romeo is unfazed and begs the Friar to perform the wedding ceremony.

When and where and how
We met, we wooed and made exchange of vow,
I’ll tell thee as we pass, but this I pray:
That thou consent to marry us today.

The Friar isn't thrilled about the marriage, but the Friar does agree to the plan; however, it isn't necessarily to make Romeo and Juliet happy. The Friar agrees to the wedding because he believes that Romeo and Juliet's forbidden love might be the thing that helps the two warring families come to peace with each other.


But come, young waverer, come, go with me,
In one respect I’ll thy assistant be,
For this alliance may so happy prove
To turn your households' rancor to pure love.

Discuss how "The Story of an Hour" depicts man vs. man.

The conflict within "The Story of an Hour" that encompasses man versus man must not be read literally as "man," but as humankind. In the story, the narrator reflects on marriage and observes that it is an institution in which there is a "blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature." In other words, Chopin was exploring the idea that when people enter marriages, sometimes they believe it empowers them to feel as if they own or control their spouses. The story suggests that marriage is especially oppressive for women because of societal expectations for them, seen in how Brently Mallard and Richards take control of the situation that Louise and her sister Josephine could likely handle on their own. The men infantilize the women and likely never would have come to the conclusion that Louise could have felt free instead of devastated if her husband had died.

In this story, we see a conflict between Louise Mallard and her husband, Brently, without his even being present: in this way, we experience a conflict that could be described as character vs. character (a more gender-inclusive way of expressing the conflict). Upon learning that her husband has been killed in a railroad accident, Louise evidently begins to feel something a lot like relief. The narrator says of her,

There would be no one to live for her during those coming years; she would live for herself. There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature.

Louise has, apparently, felt incredibly oppressed by her marriage. Though her husband himself was kind and loving toward her, the institution of marriage granted him legal and, in practice, social authority over her. She now hopes to live a long life during which she can enjoy her newfound "free[dom]," and the narrator says that "It was only yesterday she had thought with a shudder that life might be long." She didn't enjoy living her life before, but now she anticipates years of happiness. Because of this antagonism between Louise and her husband (who is, in some ways, the agent of society), one might classify the story's conflict as one of character vs. character. However, it is possible to argue that the conflict is character vs. society as well.

How is Jerry connected to the boys in the story?

This is a really interesting question because an initial snap judgement might say that Jerry and the boys are not connected. They share no dialogue with each other (because they speak different languages), and their physical time together is very minimal. Jerry is on vacation with his mother, and he asks if he can head over toward some rocks and the local beach. She reluctantly agrees, and Jerry comes across some local boys. He desperately wants to be with them. We aren't sure why it is so important to Jerry, but he definitely wants to be a part of the group of young adventurous boys.

They were of that coast; all of them were burned smooth dark brown and speaking a language he did not understand. To be with them, of them, was a craving that filled his whole body. He swam a little closer; they turned and watched him with narrowed, alert dark eyes. Then one smiled and waved. It was enough. In a minute, he had swum in and was on the rocks beside them, smiling with a desperate, nervous supplication. They shouted cheerful greetings at him;

The native boys figure out that Jerry is a foreign visitor, but they do let Jerry swim with them. Jerry is proud.

He dived, and they watched him; and when he swam around to take his place, they made way for him. He felt he was accepted and he dived again, carefully, proud of himself.

Eventually, the boys dive down and through a tunnel, and Jerry simply can't make the swim. The boys never rejoin Jerry, and he feels saddened by their departure and his own failure. That's it for the physical and visual connection between Jerry and the boys; however, that is not what is most important about the interaction. The entire episode serves as a motivator for Jerry to train and push himself hard over the next week to make that swim. Without those boys, Jerry's coming of age story wouldn't have happened. He accomplished a monumental feat. He attained a goal for himself and gained some independence in his abilities, and he's a changed boy by the end.

The only connection Jerry has to these boys comes from the fact that he was swimming at their regular beach.  When his mother went off to the touristy beach that she and Jerry used to both visit on earlier vacations, Jerry went to the "wild bay" where some older, local boys shortly came to play.  They were old enough that they seemed like men to Jerry, and he ardently wished to be accepted by them.  When they began to swim through the tunnel in the rock, he panicked that he could no longer keep up (and thus fit in) with them, and he began to clown around in a feeble and childish attempt to retain their attention.  After seeing this behavior, the boys left him behind and went away, wounding his pride and causing him to cry.  This experience prompted Jerry to spend the remainder of his vacation training to swim through the tunnel that the boys had already conquered.

How did railroads impact the settlement of the west around 1864?

Under President Abraham Lincoln in 1862, the Pacific Railway Act was approved.  With most of the nation focused on the Civil War, less attention was paid to westward expansion.  In previous decades, westward expansion had been an important focus in the United States.  People traveling west had gone by covered wagon or by horse.  This way of travel was slow and was filled with obstacles.  Wagons were made of wood and could break.  Horses and oxen could become ill and die.  The journey could take from four months to over a year.
In 1869, the Transcontinental Railroad was completed.  After this, travel from the East to the West was much quicker and more efficient.  People did not have to worry about feeding livestock or repairing wagons.  Instead, they paid a fare and boarded a train to go west.  By the year 1876, one particularly fast train had a direct route from New York City to San Francisco that took about four days.  This transformed westward expansion in the United States.  New immigrants arriving in New York City could quickly and easily move west, where the population was relatively small and there were more economic opportunities.

Find d/dx ((3a-5)x^a)/(5a-4)

I assume you mean d/dx.With this being a quotient, we would use the quotient rule. With that, the top is always the hardest.In general, if we are given f(x)/g(x), the quotient rule states:d/dx of f(x)/g(x) = [g(x)*f'(x) - f(x)*g'(x)]/[g(x)*2]Following this, we would need the derivative of the top and the bottom. So:d/dx (3a-5)x^a = a(3a-5)x^(a-1)d/dx (5a-4) = 0 (when it's with respect to x, it's like "a" is a constant. So, this would be like taking the derivative of "6.")So, combining everything:d/dx (3a-5)x^a/(5a-4) = [(5a-4)a(3a-5)x^(a-1) - (3a-5)x^a*0]/(5a-4)^2 = (5a-4)a(3a-5)x^(a-1)/(5a-4)^2And, then, you can factor out a (5a-4), for. . . = a(3a-5)x^(a-1)/(5a-4)Which would be the same as if you took everything with the "a's" in the parenthesis as one factor. As in. . .
(3a-5)/(5a-4) ---> K, so ((3a-5)x^a)/(5a-4) ---> Kx^aThe d/dx of this is. . .a*K*x^(a-1)Replace the K with (3a-5)/(5a-4), we get the same answer.

Who is Kapu's mother?

Kapu’s mother is Silver. Kapu and her mother are wolves. Their names are given to them by Miyax, who has lost her way on the northern slopes of Alaska. Miyax is the daughter of Kapugen, a great Eskimo hunter. She loses her way after running away from her husband Daniel. It is then that she comes across a pack of wolves in a region covered by large amounts of grass and moss. She sets camp temporarily near the wolves with the aim of sharing their food. She names the adult wolves Amaroq, Silver, Nails, and Jello. Amaroq is the leader of the pack and Silver’s mate. Kapu is the leader of the five puppies. Miyax calls him Kapu after her father. She calls him this because she thinks that he is “smart and fearless,” just like her father.

What is the definition of Romantic poetry?

It's not possible to provide a hard and fast definition of Romantic poetry, but we can still identify some notable characteristics all the same. The Romantic approach to poetry was marked by a tendency to abandon the quite formal, rigid standards of Neo-Classicism, both in relation to prosody and subject matter. The Romantics consciously broke with this tradition, creating an entirely new poetic language of their own.
Up until the late 18th century or so, it was widely thought that poetry should strive for objectivity, emulating an unchanging natural order that provided much-needed stability and moral guidance in human lives. Unlike their Neo-Classical forbears, however, the Romantics did not attempt to mirror the world around them, but they attempted to express their individual selves. They embraced a more subjective style of poetry, one that was concerned with the unique and the strange, the unusual and the idiosyncratic. The emotional life of the poet—his loves, his feelings, his desires—became an acceptable subject matter in its own right. What had once been thought self-indulgent and eccentric was suddenly elevated to a high art form.
A notable feature of Romantic poetry, especially in the early work of Wordsworth, was the way in which it often dealt with the lives of ordinary working people. The tenets of Neo-Classicism had held that such uncultivated lives—nasty, brutish, and short—were hardly a fit subject for poetry. Yet in works such as Wordsworth's "Lucy" poems and "Resolution and Independence," we are treated to a sympathetic portrayal of the rural poor, whose harsh, stunted lives provide ample material for an elevated insight into the human condition.
The role of nature took on huge significance for the Romantics. The natural world was regarded as almost a force in its own right, complete with its own unique personality. Nature wasn't just an object of study, or something pretty to look at; it had the power to inspire, to meld with the individual poet's imagination to conjure up a deeply philosophical vision. As Wordsworth wrote in "Tintern Abbey":

And I have felt A presence that disturbs me with the joy Of elevated thoughts; a sense sublime Of something far more deeply interfused, Whose dwelling is the light of setting suns, And the round ocean and the living air, And the blue sky, and in the mind of man: A motion and a spirit, that impels All thinking things, all objects of all thought, And rolls through all things.

Neo-Classicism distrusted the imagination, seeing it as leading to flights of self-indulgent fancy. Yet for the Romantics, it was a faculty whose free exercise was essential for the creation of art. The imagination combined with nature to generate poetry of depth and sublimity, which gave the fullest expression to all elements of the human soul, both rational and instinctual. Romantic poetry was holistic, rejecting the more narrowly rationalistic approach of Neo-Classicism to embrace the whole person.

Romantic poetry was written by European and American poets beginning around the turn of the nineteenth century and lasting till approximately mid-century. As a literary movement, Romanticism was a reaction against what preceded it, Neoclassicism, and the more rational ideas of the Enlightenment. Romantic poetry idealized Nature, man's imagination, emotions, intuitive ways of gaining knowledge, spirituality, the supernatural, and an appreciation for history. Approaches to the subject of poems tend to be subjective rather than objective, and adherence to established forms and metrical regularity is common. Many of the more well-known Romantic poems were British, such as Blake, Wordsworth, Keats, and Shelley. American Romantics include Whitman, Dickinson, Longfellow, Holmes, and Whittier. Ralph Waldo Emerson and other Transcendentalists are also considered Romantics, and Poe is noted for his particular interest in the Gothic.

What are the main themes of the novel The Years with Laura Diaz?

The Years with Laura Diaz by author Carlos Fuentes focuses on multiple themes, including censorship, art, and identity.
Censorship and Artistry
The story is narrated by Laura's great-grandson, Santiago, a photographer and filmmaker who takes a significant interest in art throughout Mexican history. At the beginning of the story, Santiago views two murals created by his grandmother's friends, both of whom were heavily censored at different points. One mural was ultimately destroyed due to its controversial themes. The story also touches on the era of censorship in the 1950s through an American political exile who becomes Laura's lover. Laura herself finds freedom in artistic expression through photography, demonstrating the duality of the industry's nature. Art can be freeing in its truest form but stifling when it is censored. 
Identity
Identity is another major theme presented throughout The Years with Laura Diaz. Laura finds herself in the position of a side character in her own story. It is only when Laura reaches her sixties after losing her lover to the communist witch hunts that she emerges as a major character in her own life. This theme is foreshadowed in an early passage of the story in which Laura's grandmother warns her to take risks to avoid living a life of regret. Laura's grandmother herself once fell in love with a dashing bandit and has always regretted not running away with him. She cautions Laura not to lose herself by being afraid of making mistakes and to take control of her own destiny. Unfortunately for Laura, she does not follow this advice until much later in life.
https://www.publishersweekly.com/978-0-374-29341-3

what novel? 

Text A Excellent, Distinguished Delegates, Ladies and Gentlemen. It gives me a great pleasure to extend to you all a warm welcome on behalf of the Ministry of Education and to say how grateful we are to all the stakeholders: educators, parents, and pupils for gracing this occasion. As you all know, today marks an important day for those Grade 12 learners who have achieveed exceptionally high metric results. We have gathered here today to acknowledge and congratulate them on their hard work and academic excellence. Read Text A above. Explain the aspects of context of the situation in reference to each of the following: Field (what is the topic of the text?) Mode (is the text spoken or written?) Tenor (who is involved in creating the text; speaker/listener?)

The field of the text is its topic; in this case, the topic is the ceremony to congratulate the seniors who have achieved high results because of their hard work. The mode is both written and oral, as the speech was written but is delivered orally. The text is mainly meant as an oral presentation. With regard to tenor, there are different people involved in giving and listening to the text. The text is likely written by a principal or superintendent in the Ministry of Education. The listeners are other people in the Ministry of Education and other "stakeholders," who are people interested in the outcome of an event or process. Stakeholders in education include teachers, parents, and students who are listening to the speech. Both the speaker and listeners help to create the text when it is read out loud. 

What terrible comment does Ko make toward her sister Yoko?

Ko says a lot of deeply unpleasant things to her little sister. She can be quite bossy at times, especially during those tense moments when everyone's feeling the pressure. Given the parlous situation Ko and her family find themselves in, it's not surprising if she occasionally lets her mouth get the better of her and says hurtful things to Yoko.
One such example comes in chapter 5 when Ko cruelly tells Yoko that their journey would've been easier had she been killed. Strictly speaking, that's probably true, but it's still a pretty unpleasant thing to say all the same. But actions speak louder than words. And throughout their terrifying ordeal, Ko shows how much she really cares for Yoko by risking her life to scavenge food and protect her family from refugees, soldiers, and anyone else who might present a threat.

To what extent do you agree that Philip Larkin presents women in his poetry as repeating familiar cultural stereotypes?

Philip Larkin's poetry could be defined by its morose tone. This negativity is often the consequence of an experience that the speaker of many of the poems has had with a woman. The mention of these women and the problems they cause the speaker could be a repetitive reliance on a stereotype, but Larkin's letters reveal that his life was actually full of troubled relationships with women; these problems started with his mother and continued on into adulthood with his difficult relationships with women who were love interests.
Because Larkin's letters reveal truths about his connection to specific women in his life, which may explain the patterns in his poetry, it is difficult to say whether or not the women in his poems are merely familiar tropes and stereotypes. Though art can sometimes mimic life, to say that Larkin's writings are all emotional expressions of his own ambivalence is also debatable. It is most likely that the answer to this question lies somewhere between the notion of the women in the poems as based on real life and the notion that they are simply symbolic of the challenges many men face in relation to women.

Of what is President Eisenhower grateful concerning Congress? Do you believe that our current Congress works in a similar cooperative or collaborative way? Explain.

When President Eisenhower gave his farewell address to the nation, he talked about how grateful he was that he was able to get along with Congress to get things done. He believed that the American people wanted the President and the Congress to work together. He believed that because his relationship with Congress was good, many things got accomplished to help the nation move forward.
Today, there seems to be less cooperation between Congress and the President. Part of the reason is that some members of Congress know they will be reelected because some congressional districts have been gerrymandered to such a degree that it is virtually guaranteed that one party will almost always win that seat in Congress. The boundary lines for these districts are drawn in such a way to make the area either very Democratic or very Republican. As a result, there is little incentive to compromise because these representatives know that if they do what the people in their district want, they will get elected even if it means little will get accomplished in Washington, DC. A good example of this is the lack of action taken regarding confirming the appointment of Justice Merrick Garland for the United States Supreme Court. Many Republicans in the Senate have said they won’t take action on his nomination until after the election in November, even though Justice Garland was nominated in March. They are hoping the Republicans will win the election for the presidency, which would allow a more conservative justice to be nominated.

What are five traumatic events in The Absolutely True Diary of a Part-Time Indian?

It seems the entire novel is one traumatic event after another for Junior as he deals with bullies, death, and his attempts to have a normal teenage life. Here are five traumatic events from the book in chronological order.
Changing Schools
Not only does Junior make a life-altering decision to change schools, but this switch involves race. Junior will now be attending a white school over 20 miles away from his home. This choice causes his tribe to hate him, and even his best friend, Rowdy, beats him up when Junior reveals his new life plan. Now he will enter a new environment without any friends.
Halloween
Junior gets beaten up and robbed on Halloween night as he ironically tries to collect money for the "poor." Not only is he hurt, but he is dealing with the trauma of poverty that, at this point, Penelope is ignorant of.
The Death of His Grandmother
Junior's grandmother was hit and killed by a drunk driver. She dies during surgery. Her last words were to forgive the person who hit her. Junior has to deal with the loss of his biggest supporter on top of forgiving the person who causes this reckless accident.
The Death of Eugene
Eugene was shot in the face in a parking lot over the last drink in a bottle of wine. The friend who shot him was so drunk, he doesn't remember shooting Eugene. Eugene, like Junior's grandmother, was someone Junior could count on. He has now lost another confidant.
The Death of Mary
His sister, Mary, and her husband threw a party in their trailer. It caught on fire, and his sister burned to death because she was too intoxicated to know what was happening. Not only does Junior face this loss, but he has to acknowledge the deeper issues of Native Americans and the reasons alcoholism runs rampant across the country.

Five traumatic events that occur in the story are:
1) When Junior tells his best friend, Rowdy, that he will be attending Reardan, Rowdy loses his temper. He is so pained by Junior's decision that he lets out his anguish in a shattering scream. Junior tells us that it is the worst thing he has ever heard. Because Rowdy feels powerless to change Junior's decision, he resorts to violence; he shoves Junior and eventually punches Junior in the face. Junior is devastated that he was beaten up by his best friend of fourteen years. This confrontation between Junior and Rowdy is one of the most traumatic events in the story.
2) Junior gets beaten up by Rowdy again, this time during a basketball game between Wellpinit and Reardan. In a close skirmish, Rowdy smashes his elbow into Junior's face and knocks him unconscious. This happens not long after someone lands a quarter on Junior's face, drawing blood. The game is also traumatic for Junior because all the reservation basketball fans turn their backs on him during the event.
3) In order to impress Penelope, Junior tells her that he's dressing as a homeless person for Halloween. He maintains that he's doing this to raise money for homeless Native Americans. On Halloween night, Junior manages to raise ten dollars by going door to door at the reservation. However, he is accosted by three guys on the way home. They beat him up and steal all his Halloween candy (including the ten dollars). Junior tells us that the most traumatic thing that happened to him was that the men spit on him. He tells us that it made him feel like "a slug burning to death from salty spit."
4) One of the most traumatic events that occurs in the story is the death of Junior's grandmother. Junior's grandmother was walking home from a powwow at the Spokane Tribal Community Center when she was run over by Gerald, a Spokane Indian alcoholic. What causes Junior much anguish is that, due to the accident, his grandmother died of massive internal injuries. Junior feels that his grandmother deserved better, as she had never drunk alcohol in her life.
5) The death of Junior's sister is also a tragedy in the novel. Junior is so traumatized by the nature of his sister's death that he resorts to helpless, nervous laughter in order to deal with his deep grief. Accordingly, Junior's sister and her husband passed out drunk in their trailer one night. During this time, someone (possibly a friend or visitor) tried to cook up some soup on a hot-plate. Eventually, they gave up, forgot about the project, and left the trailer. Later, the wind-blown curtains caught on the hot-plate, and a fire blazed through the trailer, killing both Junior's sister and her husband.
 

Many traumatic events occur in the life of Arnold Spirit Jr. (or simply "Junior"), the Native American protagonist of Sherman Alexie's The Absolutely True Diary of a Part-Time Indian:
Oscar, Junior's dog, gets sick. Because his family cannot afford to buy medicine for him, Junior's father shoots the dog. 
Junior and his best friend, Rowdy, get into many physical altercations, which usually involve Rowdy hurling homophobic insults at Junior and attacking him. Junior also must deal with the racist jokes of the jocks at his new high school, which causes a fight between Junior and Roger.
Junior's family friend, Eugene, is shot in the face by another man, Bobby, during a fight over who gets the last drink from a bottle of wine. Eugene dies, and Bobby doesn't remember pulling the trigger, having been so drunk. Bobby later hangs himself with a sheet while in jail.
Junior's Grandma, who he loved tremendously, is killed by a drunk driver as she was returning from a powwow.
Junior's sister dies in a fire that was started when someone left a hot plate on during a party. She was drunk at the time.

Evidence Montresor planned to kill fortunato

In Edgar Allan Poe's classic short story "The Cask of Amontillado," our narrator Montresor kills a man named Fortunato as a form of revenge. He does so by luring Fortunato into his catacombs, under the false pretense of allowing him to tast a rare type of wine called Amontillado. When they reach a sort of small crypt, Montresor puts a drunken Fortunato in chains and builds a wall, sealing Fortunato into the catacombs, and leaving him there to die. 
The fact that Montresor specifically tells us, in the very first line, that he planned to take revenge against Fortunato, can act as evidence that he planned to kill him. He also tells Fortunato that his family motto is "Nemo me impune lacessit", which essentially translates to "no one crosses me and gets away with it." However, probably the most solid piece of evidence showing that Montresor planned this killing is that he takes a trowel down into the catacombs with him. He uses this tool to build the wall that traps Fortunato, so his bringing it definitely shows that he planned to kill Fortunato in exactly this way. 

In the book You Are Not So Smart, what is McRaney asking you to believe about cognition and decision making? How does this challenge your assumptions about your thinking?

McRaney is asking you to believe your judgements are often guided by irrationality rather than by reason and that you do not always understand why you make the decisions you do. For example, you have preconceptions, biases, and shortcuts in your thinking (called heuristics) that make you prone to errors of judgment and decision making. An example is priming, when a stimulus from the past affects your current decision. In a study cited by the author, subjects were asked to remember a sinful memory. Half of the participants washed their hands, while others did not. Those who did not were more likely to agree at the end of the study to help a graduate student for no money, and the researchers posited that it was because the people who had washed their hands had unconsciously washed away their guilt. This study is an example of how the unconscious plays a powerful role in our decision making. 
The premise of the book might challenge your ideas that your decisions are always guided by logic and reason, or that you even know why you choose to make the decisions you do. Many people are surprised when they realize that illogic, the unconscious, and other forces beyond their control affect their decisions in powerful ways and that cognition is not entirely rational and conscious.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 70

You need to remember what a quadratic model is, such that:
a_n = f(n) = a*n^2 + b*n + c
The problem provides the following information, such that:
a_0 = 7 => f(0) = a*0^2 + b*0 + c => c = 7
a_1 = 6 => f(1) = a*1^2 + b*1 + c => a + b + c =6
a_3 = 10 => f(3) = a*3^2 + b*3 + c => 9a + 3b + c = 10
You need to replace 7 for c in equation a + b + c = 6 :
a + b +7 =6=> a + b = -1
You need to replace 7 for c in equation 9a + 3b + c = 10:
9a + 3b +7 = 10=> 9a + 3b = 3 => 3a + b = 1
Subtract a + b =-1 from 3a + b = 1 , such that:
3a + b - a - b= 1 + 1
2a = 2=> a = 1
Replace 1 for a in equation a + b =-1 such that:
1+ b = -1 => b = -2
Hence, the quadratic model for the given sequence is a_n = n^2 - 2n + 7.

In "The Necklace," how has hard work affected Mathilde's character? How has her attitude changed at the end ?

Hard work affects Mathilde's personality, physical appearance, and character in Guy De Maupassant's short story, "The Necklace." She is a dynamic character in this story that goes through several changes. 
Mathilde Loisel is described as a pretty young woman with delusions of grandeur. She is born to a modest family but covets social status and the respect that accompanies it. An example of her distaste for her station in life is contained in the following quote: 

"She had no clothes, no jewels, nothing. And these were the only things she loved; she felt that she was made for them. She had longed so eagerly to charm, to be desired, to be wildly attractive and sought after. She had a rich friend, an old school friend whom she refused to visit, because she suffered so keenly when she returned home. She would weep whole days, with grief, regret, despair, and misery."

Mathilde's husband, a lowly clerk she "allowed herself to be married to," comes home one day with an invitation to an exclusive event held by important people. He believes this will greatly please his wife, but she is not happy. She complains that she has nothing to wear, so her husband offers to give her the 400 francs he had been saving to buy himself a gun. Next, she complains because she has no jewels. Her husband suggests she borrow some from her old school friend, Madame Forestier. She borrows a beautiful diamond necklace from her friend to wear to the ball. At the ball, she is described as ecstatically happy, rejoicing in the attention she receives from men. She is charming, "quite above herself with happiness." She stays deep into the night dancing, while her husband dozes in a nearby room. 
When it comes time to leave, she is embarrassed at the wrap her husband has brought. She sees the other women with expensive furs and believes her own wrap will clash with her jewels and gown and belie her humble station in life. It is her vanity and pride that cause her to leave the party without a wrap, and she and her husband end up shivering in the cold without transportation. The tale is a bit Cinderella-esque in its description of Mathilde's gaiety at the ball, and when it is over, she is left without adornment in a shabby carriage that isn't allowed in Paris during the day.  
Mathilde doesn't notice the necklace is missing until they arrive back at home. Horrified, she and her husband concoct a plan to buy a new necklace to return to Madame Forestier without divulging the fact that the original has been lost. It is again her pride that causes her to make this choice, rather than admitting to her friend that the necklace is lost.   
Mathilde and her husband spend ten years working off the debt of thirty-four thousand dollars they incur by buying the replacement necklace.Mathilde changes physically in that time. The text describes her this way:

"Madame Loisel looked old now. She had become like all the other strong, hard, coarse women of poor households. Her hair was badly done, her skirts were awry, her hands were red. She spoke in a shrill voice, and the water slopped all over the floor when she scrubbed it."

Her character changes, as well. She accepts her lot in life and the responsibility to pay off the debt. Ironically, her pride, which would not let her tell the truth, also allows her to become everything she detested in order to pay off the debt of the replacement necklace. She honors this debt at all costs. Her servant is dismissed, she gives up her home for a modest garret under a roof. She has to haggle for everything she buys and accounts for every penny.  
When she sees Madame Forestier ten years later, she is finally prepared to reveal the true story of what happened that night. The debt has finally been paid, so she has completed her duty. She tells Madame Forestier how she has suffered in her efforts to replace it. She talks about her sufferings matter-of-factly, which is different from the beginning of the story. The littlest indignities were blown completely out of proportion in describing the way she suffered in the beginning.  
Rather than trying to climb to a higher social status, now, she accepts her fate in a lower social station than she had when she married. She is resigned, hardened, and matter of fact, rarely giving sway to the fantasies of her youth. She doesn't harbor bitterness or envy any longer. The story ends with Madame Forestier revealing that the necklace was not made of genuine diamonds, and was worth at most five hundred francs. The reader is not privy to Mathilde's response, and must make inferences about how she reacts to this news. But in the ten years since the necklace went missing, Mathilde has changed both physically and intrinsically. It's interesting to ponder how she may have reacted. 

Are there long paragraphs of description in "The Adventure of the Speckled Band" by Sir Arthur Conan Doyle, and what purpose do they serve?

There is a lengthy descriptive paragraph when Helen Stoner describes for Holmes and Watson the events on the night of her twin sister's death. The paragraph recounts the circumstances surrounding the attack which kills her, thereby providing exposition for the reader and moving the narrative along, as well as delivering the first notable clues for Holmes and Watson. The metallic sound, the low whistle, and the sight of the "speckled band" are vague hints that Holmes immediately begins working on in his formidable mind.
The paragraph that describes Dr. Grimesby Roylott is also lengthy and offers a complete portrait of his physical look from his birdlike face to his gaiters, frock coat, and black top hat. His face is described as "marked with every evil passion" to assist in his characterization.
A third lengthy paragraph of description makes clear to the reader what the setting of the bedroom in Helen Stoner's home looks like. As Holmes sits, taking in every detail of her apartment, the reader receives a strong visual. This will become important in understanding how the murder of Miss Stoner's twin took place in the house and left no trace.

How do Ivan and the general contrast with each other in "The Most Dangerous Game"?

On the surface, these two characters could not be more different. Ivan is a great, hulking brute of a man with a great beard. He is also incapable of speech as a deaf-mute and gives off a grotesque vibe. In contrast, General Zaroff is described as handsome and cultured. He has a "cultivated voice" and possesses all the charms of an aristocrat when he first meets Rainsofrd.
Though General Zaroff is more cultured and erudite than Ivan, not to mention his social superior, deep down both are sadistic brutes. General Zaroff's sophistication is only a veneer which hides his animalistic cruelty. It turns out he and Ivan are truly kindred spirits, taking pleasure in inflicting pain and viewing other human beings as prey.

Physically, the contrasts are enormous. But then, Ivan contrasts with pretty much everyone on the physical level, being such a massive great hulk of a man. As a deaf mute, he's unable to speak, so inevitably lacks the eloquence of his master, the General. Zaroff is also quite a handsome fellow, in stark contrast to the gigantic man mountain Cossack with a long black beard down to his waist.
Zaroff may be a complete psychopath with a total disregard for human life, but he still retains the polished manners of a European aristocrat. Ivan doesn't really go in for manners much. But then he doesn't need to; he's just there to frighten, intimidate, and generally act as Zaroff's all-purpose thug. A giant he may be, but gentle he is not. Ivan takes after the General in getting a kick out of hurting people, except he's much less good at hiding it than his slick, sophisticated master.

What was significant about the Battle of Normandy?

The Battle of Normandy, which began with the Anglo-American assault on the Normandy coast on June 6, 1944 (D-Day), was significant because it marked the opening of the Western front in Europe. Nazi Germany, which previously had to contend only with the Soviet Union in the East (and, to a far lesser extent, the United States in Italy) was forced to fight a two-front war. After establishing a beachhead on D-Day, the Allies drove fairly quickly through northern France, liberating Paris. After a daring and massive German counterattack was driven back in the Battle of the Bulge in late 1944 and early 1945, Germany was permanently placed on the defensive. The Normandy invasion thus marked not only a major turning point in the war, but a real death blow to Germany, which faced invading armies from the east and the west. 
https://www.history.com/topics/world-war-ii/d-day

What takes place when Jack, Ralph, and Simon find a piglet caught in the bush in Lord of the Flies?

This occurs early in the novel, as the boys are exploring and adjusting to the island. Although all three boys are hungry, when they find the trapped piglet, Jack hesitates to kill it. It is squealing in terror, and they all feel the "enormity" of killing a helpless creature and watching its blood flow. Jack's hesitation is long enough for the piglet to escape.
Afterwards, Jack is ashamed of himself for his scruples and decides that:

Next time there would be no mercy.

This passage is significant. Not only is it exciting and suspenseful, but it shows that the veneer of civilization does not fall off all at once. Jack is, at the start of the novel, a civilized boy who is inhibited about killing and feels empathy for a helpless creature. It is only over time that he will lose that and discover his atavistic, primal self.
The episode both foreshadows and acts as a contrast to the more memorable and savage pig killing that is to come.

Towards the end of chapter one, Ralph, Jack, and Simon are returning to the platform after exploring the island, when they come across a piglet that is caught in the creepers. The boys rush towards the defenseless, squealing piglet, and Jack proceeds to draw his knife.
Before Jack brings his knife down, he hesitates for a moment and allows the piglet to escape. The boys are astonished by Jack's hesitation, and he makes an excuse by telling Ralph and Simon that he was having difficulty choosing the correct place to strike the pig. When Ralph asks Jack why he did not simply stab the pig, Golding writes,

They knew very well why he hadn’t: because of the enormity of the knife descending and cutting into living flesh; because of the unbearable blood. (41)

Jack's hesitation is significant and emphasizes the boys' civility. They have recently landed on the remote, tropical island and have not adjusted to living in the wilderness. Jack is not yet willing to stab the pig and experience an immense amount of blood. He is still very much influenced by civilization and English society, where hunting and blood are foreign to him.
This scene also establishes a starting point and allows the audience the gauge the boys' diminishing civility and propensity for violence as the story progresses.

Because the boys have only recently arrived on the island, when Simon, Ralph, and Jack encounter the piglet, they fail at their attempts to kill it.
As the boys gather together in their response to the conch, Ralph, having been voted leader, chooses Jack and Simon to help him explore the area and determine whether they are actually on an island. After climbing for a time, they discover a pink coral mountain and see that they are, indeed, on an island. Following their satisfying a temptation to roll boulders down the mountain, the boys see the tracks of an animal that they cannot yet identify. Ebullient as they descend the mountain, Ralph spreads his arms, crying out, "All ours."
As the threesome enter a thick forest, they hear squealing noises. Growing nearer, the boys hear the frenzy of a piglet caught in the "curtain of creepers." Jack draws his knife "with a flourish," but hesitates at this, his first attempt at killing: 

The pause was only long enough for them to understand what an enormity the downward stroke would be. (Ch.1)

In this short pause, the piglet manages to free itself and scurry into the undergrowth. The boys simply stare at each other; Jack's face is white beneath his freckles, the enormity of the act having overcome him. All three of the boys laugh nervously and "ashamedly." Then they climb back to the path.
This incident is the boys' first real experience of life in the wild. Because they are not yet adapted to this new environment, Ralph, Simon, and Jack pause as they stand between these two worlds. Resolved that "[N]ext time there would be no mercy," Jack shoves his knife into a tree trunk in a show of manliness as he dares the others to contradict him.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 4

a.) Determine $y'$ by Implicit Differentiation.
b.) Find the equation explicitly for $y$ and differentiate to get $y'$ in terms of $x$.
c.) Check that your solutions to part (a) and (b) are consistent by substituting the expression for $y$ into your solution for part (a).

a.) Given: $\cos x + \sqrt{y} = 5$
$\displaystyle \frac{d}{dx} ( \cos x) + \frac{d}{dx} (\sqrt{y}) = \frac{d}{dx}(5)$
$\displaystyle \frac{d}{dx} (\cos x) + \frac{d}{dx} (y)^{\frac{1}{2}} = \frac{d}{dx}(5)$

$
\begin{equation}
\begin{aligned}
-\sin x + \frac{1}{2}(y)^{- \frac{1}{2}} \frac{d}{dx}(y) &= 0\\
\\
-\sin x + \frac{1}{2}(y)^{- \frac{1}{2}} \frac{dy}{dx} & = 0 \\
\\
-\sin x + \left( \frac{1}{2\sqrt{y}}\right) \frac{dy}{dx} & = 0\\
\\
\left( \frac{1}{2\sqrt{y}}\right) \frac{dy}{dx} & = \sin x\\
\\
\frac{dy}{dx} &= 2 \sqrt{y} \sin x && \text{(Equation 1)}
\end{aligned}
\end{equation}
$


b.) Solving for $y$

$
\begin{equation}
\begin{aligned}
\sqrt{y} &= 5 - \cos x \\
\\
(\sqrt{y})^2 &= (5 - \cos x)^2\\
\\
y & = (5- \cos x)^2 && \text{(Equation 2)}\\
\\
\frac{d}{dx} (y) & = \frac{d}{dx} ( 5- \cos x)^2\\
\\
\frac{dy}{dx} & = 2 (5- \cos x) \frac{d}{dx} (5- \cos x)\\
\\
\frac{dy}{dx} & = 2 (5 - \cos x ) \left[ 0 - (-\sin x) \right]\\
\\
\frac{dy}{dx} & = 2 (5 - \cos x ) ( \sin x ) \qquad \text{ or } \qquad y'=2(5-\cos x)(\sin x)
\end{aligned}
\end{equation}
$

c.) Substituting Equation 2 in Equation 1

$
\begin{equation}
\begin{aligned}
y' & = 2\sqrt{y} \sin x && \text{(Equation 1)}\\
\\
y &= (5-\cos x)^2 && \text{(Equation 2)}\\
\\
y' &= 2 \sqrt{(5-\cos x)^2} \sin x\\
\\
y' &= 2 (5-\cos x) \sin x
\end{aligned}
\end{equation}
$

Results from part (a) and part (b) are equivalent.

What effect does Daisy's daughter have on Gatsby?

Gatsby seems short of shocked when he meets Pammy, Daisy's young daughter. Daisy greets her child, crooning to her and encouraging a hug, and then the little girl meets Gatsby and Nick, shaking each of their hands in turn. Of this moment, Nick says,

Afterward, [Gatsby] kept looking at the child with surprise. I don't think he had ever really believed in its existence before.

Despite the fact, then, that Gatsby knows Daisy has a daughter with her husband, Tom, Gatsby still seems surprised when faced with proof of her actual, physical person. Gatsby is really adept at living within his imagination: for all these long years, he's convinced himself that one can absolutely relive the past, that it is, in fact, possible for him and Daisy to return to the people they once were before she married Tom. However, the fact of this child's existence kind of ruins that fantasy, because, even if Daisy were to leave Tom for Gatsby, Daisy's daughter would, in all likelihood, come with her. This means that it wouldn't just be the two of them—Gatsby and Daisy—as they were before the war; Pammy would always be a reminder of their time apart and the things that did, indeed, permanently change in Daisy's life as a result of her marriage.

How can I write an analytical essay on "Big Black Good Man" by Richard Wright?

A successful literary analysis begins with careful close readings of the literary work, in this case, the short story "Big Black Good Man" by Richard Wright (1908-1960), published posthumously in the collection Eight Men (1961). A successful analysis will examine and discuss background information (e.g., historic, social, author biography) and the opinions of critics and scholars. The nugget of a literary analysis essay expresses your own textual analysis and your critical argument expressing your own idea about the story. Your idea must be developed and supported directly from the words of the text, and this text must be clearly presented and soundly explicated.An example of an idea about the text that might be expanded into a literary analysis is the question of what psychological reaction changed the attitude of the big black good man at the very end of the short story; it is his attitude change that drives the dramatic twist and surprise ending. Understanding and presenting the literary analysis of the man's original attitude and change in attitude will call for examining the text to substantiate the sincerity of his earlier attitude and of his apparent surprise at the fear he had lodged in Olaf's mind. This analysis will also call for examining the character development given to the big black good man to determine what his emotional and cognitive responses, unstated but implied in the text, might have been.

   "Thanks!" Olaf cried after him.   The black giant paused, turned his vast black head, and flashed a grin.   "Daddy-O, drop dead," he said and was gone.

Following this type of examination of the text to analyze and understand characterization development, motivation for actions, psychological reactions and any other relevant textual elements, such as setting, tone, mood, etc., will provide the framework for a literary analysis essay examining any question you may develop for "Big Black Good Man."
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